of course it's converted to AC.. you need to do that to use it in your house anyway.

Well DC is only used for HVDC lines as far as I know, at least day to day for most people.

people without batteries rely on net metering. They use to solar panels during the day to either reduce the amount of power they get from the power company or they even produce a surplus during the day and send some back up the line for local distribution. This reduces their power bill but they still rely power company for power since for safety reason they have the aforementioned power cut off so line workers aren't zapped. So no you generally can't use your panels if you are grid connected with no batteries though in theory you would just manually disconnect from the grid and power the house during the day depending on how much you generate and how much you need.

For those with a battery but are connected to the grid it's a bit different. They of course use the panels to power their house but also charge up batteries for later use and once the batteries are full send power back to the grid. They of course use the batteries at night or during inclement weathers when there isn't much sun. If the power from the grid goes out they can instantly switch to solar, battery or a combinations of the two depending on the circumstances.